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2017 Information loss on Gaussian Volterra process
Arturo Valdivia
Electron. Commun. Probab. 22: 1-5 (2017). DOI: 10.1214/17-ECP79

Abstract

Gaussian Volterra processes are processes of the form $(X_{t}:=\int _{\mathbf{T} }k(t,s)\mathrm{d} W_{s})_{t\in \mathbf{T} }$ where $(W_{t})_{t\in \mathbf{T} }$ is Brownian motion, and $k$ is a deterministic Volterra kernel. On integrating the kernel $k$ an information loss may occur, in the sense that the filtration of the Volterra process needs to be enlarged in order to recover the filtration of the driving Brownian motion. In this note we describe such enlargement of filtrations in terms of the Volterra kernel. For kernels of the form $k(t,s)=k(t-s)$ we provide a simple criterion to ensure that the aforementioned filtrations coincide.

Citation

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Arturo Valdivia. "Information loss on Gaussian Volterra process." Electron. Commun. Probab. 22 1 - 5, 2017. https://doi.org/10.1214/17-ECP79

Information

Received: 2 January 2017; Accepted: 9 August 2017; Published: 2017
First available in Project Euclid: 25 October 2017

zbMATH: 06797813
MathSciNet: MR3724558
Digital Object Identifier: 10.1214/17-ECP79

Subjects:
Primary: 60G22, 60H20, 60J65, 91G99

JOURNAL ARTICLE
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